This paper presents our submissions for the CoNLL 2017 UD Shared Task. Our parser, called UParse, is based on a neural network graph-based dependency parser. The parser uses features from a bidirectional LSTM to produce a distribution over possible heads for each word in the sentence. To allow transfer learning for lowresource treebanks and surprise languages, we train several multilingual models for related languages, grouped by their genus and language families. Out of 33 participants, our system achieves rank 9th in the main results, with 75.49 UAS and 68.87 LAS F-1 scores (average across 81 treebanks).